Parse MOI.ScalarNonlinearFunction polynomials for HUBO/PUBO objectives and constraints

[bernalde]

Motivation

MQT QAO (arXiv:2406.12840, Sec IV-E) accepts arbitrary-degree sympy polynomial objectives, funnels them into a qubovert PUBO, and reduces degree at solve time (src/mqt/qao/problem.py:51-102, solvers.py:102-103); its XOR penalty is natively cubic (constraints.py:630-671). ToQUBO cannot accept degree-3+ input even though its internal machinery handles arbitrary degree.

Current state

src/compiler/parse.jl (186 lines) has parse! methods only for VI, SAF{T}, SQF{T} — nothing for ScalarNonlinearFunction; grep for ScalarNonlinearFunction/NLPBlock over src/ and docs/src returns zero hits. PreQUBOModel declares only VI/SAF/SQF scalar functions (src/model/prequbo.jl:10-34), so SNF support is false. Meanwhile the arbitrary-degree machinery already exists: PBF IR plus quadratize! at src/compiler/build.jl:68-82 with the residual-degree guard in output! at :100-114, and constraints already auto-set Quadratize (src/compiler/constraints.jl:535,613,635,735,757,823,938,978).

Proposed change

Purely input-side work:

1. Add parse! methods for MOI.ScalarNonlinearFunction in src/compiler/parse.jl that walk +, -, *, ^ trees over VI into PBO.PBF, erroring cleanly on non-polynomial heads (sin, /, etc.).
2. Declare SNF objective/constraint support alongside PreQUBOModel — MOIU.@model cannot list SNF, so add explicit MOI.supports/add_constraint methods like the pair-specific overrides at prequbo.jl:38-96.
3. Set Attributes.Quadratize() when parsed degree > 2.

Note: copy_to at src/wrapper.jl:88-94 sets the objective on a full_bridge_optimizer without a supports check — verify the error/bridge path across supported MOI versions.

Acceptance criteria

• A cubic JuMP objective (e.g. @objective(model, Min, x*y*z)) compiles and solves through ToQUBO with correct quadratized target model.
• Degree-3+ polynomial equality/inequality constraints compile.
• Non-polynomial SNF heads produce a descriptive error naming the offending operator.
• Quadratize is auto-enabled for degree > 2 input; tests assert final target degree ≤ 2.

Part of the MQT QAO parity epic: JuliaQUBO/QUBO.jl#69